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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Traveling waves of the spread of avian influenza


Authors: Zhi-Cheng Wang, Jianhong Wu and Rongsong Liu
Journal: Proc. Amer. Math. Soc. 140 (2012), 3931-3946
MSC (2010): Primary 35K57, 92D30; Secondary 34K10
Published electronically: March 22, 2012
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Abstract: This paper gives a proof for the existence and nonexistence of traveling wave solutions of a reaction-convection epidemic model for the spatial spread of H5N1 avian influenza involving a wide range of bird species and environmental contamination. The threshold condition for the existence of traveling waves coincides with the basic reproduction number exceeding one. The existence of wave solutions is obtained by constructing an invariant cone of initial functions defined on a large spatial domain, applying a fixed point theorem on this cone and then a limiting argument. The invariant cone is based on the information of initial growth pattern of the epidemic and the final size estimation during the entire course of the outbreak.


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Additional Information

Zhi-Cheng Wang
Affiliation: School of Mathematics and Statistics, Lanzhou University, Lanzhou, Gansu, 730000, People’s Republic of China
Email: wangzhch@lzu.edu.cn

Jianhong Wu
Affiliation: Centre for Disease Modeling, York Institute for Health Research and Department of Mathematics and Statistics, York University, Toronto, Ontario, M3J 1P3, Canada
Email: wujh@mathstat.yorku.ca

Rongsong Liu
Affiliation: Department of Mathematics and Department of Zoology and Physiology, University of Wyoming, Laramie, Wyoming 82072
Email: Rongsong.Liu@uwyo.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-2012-11246-8
PII: S 0002-9939(2012)11246-8
Keywords: Disease spread, avian influenza, epidemic wave.
Received by editor(s): January 26, 2010
Received by editor(s) in revised form: May 11, 2011
Published electronically: March 22, 2012
Additional Notes: The first author was supported in part by the NSF of China (11071105), by FRFCU (lzujbky-2011-27) and by the Program for New Century Excellent Talents in University (NCET-2010-0470).
The second author was supported in part by CRC, NSERC, CIHR, MITACS and GEOIDE
The third author was supported in part by the University of Wyoming’s EPScoR start-up fund.
Communicated by: Yingfei Yi
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.